Question

The linear speed of a stone revolving 5 times in a circle of 4 cm radius in 2 minute is (in $cm s^{-1}$)

• A. $\frac{\pi}{4}$
• B. $\frac{2\pi}{4}$
• C. $\frac{\pi}{2}$
• D. $\frac{3\pi}{4}$
• E. $\frac{\pi}{3}$

Hint:

Always convert time to seconds for standard speed calculations.

Answer 1

Answer: (E)

Step 1: Concept
Linear speed ($v$) = $\frac{\text{Total Distance}}{\text{Total Time}}$.

Step 2: Meaning
Distance for 5 revolutions = $5 \times 2\pi r$. Time = 120 seconds.

Step 3: Analysis
Distance = $5 \times 2\pi \times 4 = 40\pi$ cm.
Speed $v = \frac{40\pi}{120} = \frac{\pi}{3} cm s^{-1}$.

Step 4: Conclusion
Hence, the linear speed is $\frac{\pi}{3}$.
Final Answer: (E)